Kalman Filter Data Assimilation Scheme Research Articles

Reconstructing cardiac electrical excitations from optical mapping recordings.

The reconstruction of electrical excitation patterns through the unobserved depth of the tissue is essential to realizing the potential of computational models in cardiac medicine. We have utilized experimental optical-mapping recordings of cardiac electrical excitation on the epicardial and endocardial surfaces of a canine ventricle as observations directing a local ensemble transform Kalman filter data assimilation scheme. We demonstrate that the inclusion of explicit information about the stimulation protocol can marginally improve the confidence of the ensemble reconstruction and the reliability of the assimilation over time. Likewise, we consider the efficacy of stochastic modeling additions to the assimilation scheme in the context of experimentally derived observation sets. Approximation error is addressed at both the observation and modeling stages through the uncertainty of observations and the specification of the model used in the assimilation ensemble. We find that perturbative modifications to the observations have marginal to deleterious effects on the accuracy and robustness of the state reconstruction. Furthermore, we find that incorporating additional information from the observations into the model itself (in the case of stimulus and stochastic currents) has a marginal improvement on the reconstruction accuracy over a fully autonomous model, while complicating the model itself and thus introducing potential for new types of model errors. That the inclusion of explicit modeling information has negligible to negative effects on the reconstruction implies the need for new avenues for optimization of data assimilation schemes applied to cardiac electrical excitation.

The effects of estimating a photoionization parameter within a physics-based model using data assimilation

Data assimilation (DA) is the process of merging information from prediction models with noisy observations to produce an estimate of the state of a physical system. In ionospheric physics-based models, the solar ionizing irradiance is commonly estimated from a solar index like F10.7. The goal of this work is to provide the fundamental understanding necessary to appreciate how a DA algorithm responds to estimating an external parameter driving the model’s interpretation of this solar ionizing irradiance. Therefore, in this work we allow the DA system to find the F10.7 value that delivers the degree of photoionization that leads to a predicted electron density field that best matches the observations. To this end, we develop a heuristic model of the ionosphere along the magnetic equator that contains physics from solar forcing and recombination/plasma diffusion, which allows us to explore the impacts of strongly forced system dynamics on DA. This framework was carefully crafted to be both linear and Gaussian, which allows us to use a Kalman filter to clearly see how: (1) while recombination acts as a sink on the information in the initial condition for ionospheric field variables, recombination does not impact the information in parameter estimates in the same way, (2) when solar forcing dominates the electron density field, the prior covariance matrix becomes dominated by its leading eigenvector whose structure is directly related to that of the solar forcing, (3) estimation of parameters for forcing terms leads to a time-lag in the state estimate relative to the truth, (4) the performance of a DA system in this regime is determined by the relative dominance of solar forcing and recombination to that of the smaller-scale processes and (5) the most impactful observations on the electron density field and on the solar forcing parameter are those observations on the sunlit side of the ionosphere. These findings are then illustrated in a full physics-based ionospheric model using an ensemble Kalman filter DA scheme.

Effects of estimating the ionospheric and thermospheric parameters on electron density forecasts

Based on the thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM), a thermospheric-ionospheric data assimilation and forecast system is developed. Using this system, we estimated the oxygen ions, neutral temperature, wind, and composition by assimilating the simulated data from Formosa Satellite 3/Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) occultation electron density profiles to evaluate their effects on the ionospheric forecast. An ensemble Kalman filter data assimilation scheme and combined state and parameter estimation methods are used to estimate the unobserved parameters in the model. The statistical results show that the neutral and ion compositions are more effective than the neutral temperature and wind for improving the forecast of the ionospheric electron density, whose root mean square errors in the assimilation period decreased by approximately 40%, 30%, and 10% due to the estimations of the neutral composition, oxygen ions, and neutral temperature, respectively. Due to the different physical and chemical processes that these parameters primarily affect, their e-folding times differ greatly from longer than 12 h for neutral composition to approximately 6 h for oxygen ions and 3 h for neutral temperature. The effect of estimating the neutral composition on improving the ionospheric forecast is greater than that of estimating the oxygen ions, which can be also be seen in an actual data assimilation experiment. This indicates that the neutral composition is the most important thermospheric parameter in ionospheric data assimilations and forecasts.

Evaluation on surface current observing network of high frequency ground wave radars in the Gulf of Thailand

Due to the high cost of ocean observation system, the scientific design of observation network becomes much important. The current network of the high frequency radar system in the Gulf of Thailand has been studied using a three-dimensional coastal ocean model. At first, the observations from current radars have been assimilated into this coastal model and the forecast results have improved due to the data assimilation. But the results also show that further optimization of the observing network is necessary. And then, a series of experiments were carried out to assess the performance of the existing high frequency ground wave radar surface current observation system. The simulated surface current data in three regions were assimilated sequentially using an efficient ensemble Kalman filter data assimilation scheme. The experimental results showed that the coastal surface current observation system plays a positive role in improving the numerical simulation of the currents. Compared with the control experiment without assimilation, the simulation precision of surface and subsurface current had been improved after assimilated the surface currents observed at current networks. However, the improvement for three observing regions was quite different and current observing network in the Gulf of Thailand is not effective and a further optimization is required. Based on these evaluations, a manual scheme has been designed by discarding the redundant and inefficient locations and adding new stations where the performance after data assimilation is still low. For comparison, an objective scheme based on the idea of data assimilation has been obtained. Results show that all the two schemes of observing network perform better than the original network and optimal scheme-based data assimilation is much superior to the manual scheme that based on the evaluation of original observing network in the Gulf of Thailand. The distributions of the optimal network of radars could be a useful guidance for future design of observing system in this region.

A regional ionospheric TEC mapping technique over China and adjacent areas on the basis of data assimilation

AbstractIn this paper, a regional total electron content (TEC) mapping technique over China and adjacent areas (70°E–140°E and 15°N–55°N) is developed on the basis of a Kalman filter data assimilation scheme driven by Global Navigation Satellite Systems (GNSS) data from the Crustal Movement Observation Network of China and International GNSS Service. The regional TEC maps can be generated accordingly with the spatial and temporal resolution being 1°×1° and 5 min, respectively. The accuracy and quality of the TEC mapping technique have been validated through the comparison with GNSS observations, the International Reference Ionosphere model values, the global ionosphere maps from Center for Orbit Determination of Europe, and the Massachusetts Institute of Technology Automated Processing of GPS TEC data from Madrigal database. The verification results indicate that great systematic improvements can be obtained when data are assimilated into the background model, which demonstrates the effectiveness of this technique in providing accurate regional specification of the ionospheric TEC over China and adjacent areas.

Adaptive Kalman Filtering Scheme for the Simulation of Benzene in Subsurface Environment

Accurate information about contaminant plume migration in the subsurface plays an important role in risk assessment and emergency response during site remediation. Rapid emergency response during severe soil contamination can help to reduce the extent of damage and the risk of groundwater contamination. The use of subsurface contaminant transport models, coupled with stochastic data assimilation schemes, can provide accurate prediction of contaminant transport to enhance the reliability of risk assessment in the area of environmental remediation. In this study, a two-dimensional deterministic model is used to simulate the advective and diffusive transport of benzene in the subsurface. A robust adaptive Kalman filter (AKF) is constructed as a stochastic data assimilation scheme to improve the prediction of the benzene contaminant plume. The AKF has been proposed to overcome the limitations of the conventional Kalman filter (KF) by reducing the uncertainties associated with the process and observation noise statistics. The impact of the adaptive filter on the KF performance is examined by comparing model predictions with a simulated true field, which is created by introducing random noise into an observation model. The results show that the KF data assimilation scheme can give a more accurate prediction of the benzene plume than the conventional numerical approach although its prediction accuracy is minimal in comparison to the AKF scheme. The KF scheme reduces the root-mean-square error (RMSE) of the plume estimate from 5.0 to 1.1 mg/L at the end of the 10-day simulation. Furthermore, by constructing the AKF data assimilation scheme, the prediction error of KF reduces from 1.1 to 0.9 mg/L, indicating 18% improvement in prediction accuracy. Also, the results of the sensitivity test suggest that filter stability and accuracy greatly depends on the window size, which must be specified to start the adaptive process.

US‐TEC: A new data assimilation product from the Space Environment Center characterizing the ionospheric total electron content using real‐time GPS data

The potential of data assimilation for operational numerical weather forecasting has been appreciated for many years. For space weather it is a new path that we are just beginning to explore. With the emergence of satellite constellations and the networks of ground‐based observations, sufficient data sources are now available to make the application of data assimilation techniques a viable option. The first space weather product at Space Environment Center (SEC) utilizing data assimilation techniques, US‐TEC, was launched as a test operational product in November 2004. US‐TEC characterizes the ionospheric total electron content (TEC) over the continental United States (CONUS) every 15 min with about a 15‐min latency. US‐TEC is based on a Kalman filter data assimilation scheme driven by a ground‐based network of real‐time GPS stations. The product includes a map of the vertical TEC, an estimate of the uncertainty in the map, and the departure of the TEC from a 10‐day average at that particular universal time. In addition, data files are provided for vertical TEC and the line‐of‐sight electron content to all GPS satellites in view over the CONUS at that time. The information can be used to improve single‐frequency GPS positioning by providing more accurate corrections for the ionospheric signal delay, or it can be used to initialize rapid integer ambiguity resolution schemes for dual‐frequency GPS systems. Validation of US‐TEC indicates an accuracy of the line‐of‐sight electron content of between 2 and 3 TEC units (1 TECU = 1016 el m−2), equivalent to less than 50 cm signal delay at L1 frequencies, which promises value for GPS users. This is the first step along a path that will likely lead to major improvement in space weather forecasting, paralleling the advances achieved in meteorological weather forecasting.

Distance-Dependent Filtering of Background Error Covariance Estimates in an Ensemble Kalman Filter

The usefulness of a distance-dependent reduction of background error covariance estimates in an ensemble Kalman filter is demonstrated. Covariances are reduced by performing an elementwise multiplication of the background error covariance matrix with a correlation function with local support. This reduces noisiness and results in an improved background error covariance estimate, which generates a reduced-error ensemble of model initial conditions. The benefits of applying the correlation function can be understood in part from examining the characteristics of simple 2 × 2 covariance matrices generated from random sample vectors with known variances and covariance. These show that noisiness in covariance estimates tends to overwhelm the signal when the ensemble size is small and/or the true covariance between the sample elements is small. Since the true covariance of forecast errors is generally related to the distance between grid points, covariance estimates generally have a higher ratio of noise to signal with increasing distance between grid points. This property is also demonstrated using a two-layer hemispheric primitive equation model and comparing covariance estimates generated by small and large ensembles. Covariances from the large ensemble are assumed to be accurate and are used a reference for measuring errors from covariances estimated from a small ensemble. The benefits of including distance-dependent reduction of covariance estimates are demonstrated with an ensemble Kalman filter data assimilation scheme. The optimal correlation length scale of the filter function depends on ensemble size; larger correlation lengths are preferable for larger ensembles. The effects of inflating background error covariance estimates are examined as a way of stabilizing the filter. It was found that more inflation was necessary for smaller ensembles than for larger ensembles.